Details

Time bar (total: 10.6s)

sample23.0ms

Algorithm
intervals
Results
4.0ms54×body1280valid
4.0ms269×body80nan
2.0ms143×body80valid
2.0ms39×body640valid
1.0ms11×body320valid
0.0ms9×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.1b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-exp-log sqrt-div add-cbrt-cube distribute-lft-out
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+
Counts
2 → 35
Calls
2 calls:
4.0ms
(sqrt (+ x 1.0))
21.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series105.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(sqrt (+ x 1.0))
74.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify913.0ms

Counts
41 → 41
Iterations

Useful iterations: 3 (186.0ms)

IterNodesCost
084488
1186440
2543410
32015402
done5001402

prune82.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
74×*-un-lft-identity
32×distribute-lft-out
28×sqrt-prod
24×times-frac
17×add-sqr-sqrt
16×add-cube-cbrt
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 80
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
16.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
28.0ms
(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series242.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(sqrt (+ x 1.0))
67.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
143.0ms
(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify921.0ms

Counts
89 → 89
Iterations

Useful iterations: done (918.0ms)

IterNodesCost
01631403
13891159
213861054
done50001048

prune181.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(sqrt (sqrt (+ x 1.0)))
0.2b
(/ (+ 0 1.0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.3b
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
63×add-sqr-sqrt
55×*-un-lft-identity
40×sqrt-pow1
32×sqrt-div
31×pow1
29×add-cube-cbrt
20×pow1/2
18×swap-sqr
12×times-frac distribute-lft-out
10×flip3-+ associate-*r* associate-*l* flip-+
9×pow-prod-up unswap-sqr
8×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square associate-/l* add-log-exp
3×associate-/r*
2×associate-*r/ associate-*l/ associate-/r/ associate-/l/
1×cbrt-undiv pow2 frac-2neg pow-plus sqrt-unprod div-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 167
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ x 1.0)))
5.0ms
(sqrt (sqrt (+ x 1.0)))
32.0ms
(/ (+ 0 1.0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
26.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series367.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(sqrt (sqrt (+ x 1.0)))
92.0ms
(sqrt (sqrt (+ x 1.0)))
149.0ms
(/ (+ 0 1.0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
32.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify1.7s

Counts
179 → 179
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02603210
15711949
224511808
done50001804

prune352.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
21.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
21.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
26.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
73.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series832.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
172.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
341.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
151.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify3.4s

Counts
457 → 457
Iterations

Useful iterations: done (3.3s)

IterNodesCost
044015237
1104412904
2404511576
done500011574

prune529.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 2 (1.0ms)

IterNodesCost
01118
11418
21816
done1816

end0.0ms

sample642.0ms

Algorithm
intervals
Results
138.0ms1713×body1280valid
136.0ms8101×body80nan
83.0ms1251×body640valid
73.0ms4067×body80valid
29.0ms615×body320valid
12.0ms354×body160valid